The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That is, bidding your true value is a weakly dominant strategy in SPA, whereas in FPA, bidding below your true value is the dominant strategy. See this question.
My question is: why does it matter to the seller whether people bid truthfully or not? Initially, I thought that since SPA induce truthful bidding, they also maximize expected revenue for the seller, which is why a seller would use SPA. But, according to the revenue equivalence theorem, FPA and SPA generate the same expected revenue. So, shouldn't it not matter to the seller what auction they choose? Why would a seller prefer SPA -- which are generally harder to explain -- if it doesn't generate higher expected revenue?
I can think of three possible explanations:
- There's a mismatch between theory and the real world. Maybe in theory SPA and FPA should generate the same revenue, but in practice they don't. If so, is there any empirical research that shows this?
- The seller's goal is to collect information rather than to maximize revenue. Maybe the seller has a product and they don't know how much to sell it for. In that case, an SPA could help them generate an accurate demand curve.
- To benefit the buyer. If there's no cost to the seller in terms of revenue, but a benefit to the buyer, a seller might want to use SPA. But this leads to the question: why does the seller care about helping the buyer? Maybe in order to encourage more buyers to participate in the auction? And, possibly encouraging more buyers to enter the auction would raise the expected revenue from the auction, if those new buyers were higher bidders.
Since SPA are so common in online advertising (google adwords) and eBay, they might be the most widely used auction there is today. So, I'm wondering why sellers prefer them to FPA. Is any of these explanations on the right track?